Which example best describes reducing risky behavior?

Let $S$ be the set of complex numbers of the form $a + bi,$ where $a$ and $b$ are integers. We say that $z \in S$ is a unit if t

lakkis [162]

Answer:

Number of units possible in S are 4.

Explanation:

Given S is a set of complex number of the form $a+bi$ where a and b are integers.

$z\in S$ is a unit if $w\in z$ exists such that $zw=1$ .

To find:

Number of units possible = ?

Solution:

Given that:

$zw = 1$

Taking modulus both sides:

$|zw| = |1|$

Using the property that modulus of product of two complex numbers is equal to their individual modulus multiplied.

i.e.

$|z_1z_2|=|z_1|.|z_2|$

So,

$|zw| = |1|\\\Rightarrow |zw| =|z|.|w| =1\\\Rightarrow |z|=\dfrac{1}{|w|}$ ......... (1)

Let $z=a+bi$

Then modulus of z is $|z| = \sqrt{a^2+b^2}$

Given that a and b are integers, so the equation (1) can be true only when $|z| = |w| =1$ (Reciprocal of 1 is 1). Modulus can be equal only when one of the following is satisfied:

(a = 1, b = 0) , (a = -1, b = 0), (a = 0, b = 1) OR (a = 0, b = -1)

So, the possible complex numbers can be:

$1.\ 1 + 0i = 1\\2.\ -1 + 0i = -1\\3.\ 0+ 1i = i\\4.\ 0 -1i = -i$

Hence, number of units possible in S are 4.

6 0

3 years ago

On August 1, 20Y7, Rafael Masey established Planet Realty, which completed the following transactions during the month:

Sphinxa [80]

Answer:

a. Dr Cash 17,500

Cr Common Stock 17,500

b. Dr Supplies 2,300

Cr Account payable 2,300

c. Dr Cash 13,300

Cr Sales commission 13,300

d. Dr Rent expense 3,000

Cr Cash 3,000

e. Dr Account payable 1,150

Cr Cash 1,150

f. Dr Dividend 1,800

Cr Cash 1, 800

g. Dr Automobile expense 1,500

Dr Miscellaneous expense 400

Cr Cash 1,900

h. Dr Salaries expense 2,800

Cr Cash 2,800

i. Dr Supplies expense 1,050

Cr Supplies 1,050

Explanation:

Preparation of Journal entry

a. Dr Cash 17,500

Cr Common Stock 17,500

b. Dr Supplies 2,300

Cr Account payable 2,300

c. Dr Cash 13,300

Cr Sales commission 13,300

d. Dr Rent expense 3,000

Cr Cash 3,000

e. Dr Account payable 1,150

Cr Cash 1,150

f. Dr Dividend 1,800

Cr Cash 1, 800

g. Dr Automobile expense 1,500

Dr Miscellaneous expense 400

Cr Cash 1,900

(1,500+400)

h. Dr Salaries expense 2,800

Cr Cash 2,800

i. Dr Supplies expense 1,050

Cr Supplies 1,050

8 0

3 years ago

You can buy a car that is advertised for $24,600 on the following terms: (a) pay $24,600 and receive a $4,600 rebate from the ma

Vadim26 [7]

Answer:

A. $20,000

B. $17,234.18

C.Option (b)

Explanation:

Obviously, the option with lower Present Value would be the best option to buy the car. The Present Value of the options can find out as following

REQUIREMENT A

Price of car = $24,600

Rebate = $4,600

Present value of the payments for option = Price of the car – rebate

Present value of the payments for option (a) = $24,600 - $4,600

Present value of the payments for option = $20,000

REQUIREMENT B

We can use the following Present Value of an Annuity formula to calculate the present value of the payments

PV of the payments for option = PMT * [1-(1+i) ^-n)]/i

PV of the payments for option (b) (PV) =?

Monthly payment PMT =$410 per month

Number of payments n = 5 years *12 months = 60

Monthly interest rate i=1.25% per month or 0.0125

PV of the payments for option = $410 x [1- (1+0.0125) ^-60]/0.0125

PV of the payments for option = $17,234.18

REQUIREMENT C.

Which is the better deal?

Option (b) is better deal as the present value of payments ($17,234.18) is less than Present value of the payments for option (a); $20,000.

3 0

3 years ago

Read the following email, which Jim sent to his team. Then choose the answer below that best explains what is wrong with the ema

mars1129 [50]

Answer and Explanation:

The subject of the email is too long and contains all the information. The subject should have been: Proposal draft due on Friday. Rest of the information should have been included in the body of the email.

8 0

3 years ago

Payback period is the amount of time it will take to recoup, in the form of net cash inflows, the total dollars invested in a pr

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4 0

3 years ago